Linear complementarity models for steady-state analysis of pulse-width modulated switched electronic systems

In the recent literature it has been shown how it is possible to represent electrical circuits with ideal diodes as Linear Complementarity Systems (LCSs) and, in the presence of externally controlled electronic devices, as switched LCSs. In this paper we show how it is possible to model within the non-switched linear complementarity framework also switched electronic systems which include externally controlled state-dependent switchings. The model discretization allows to formulate a static complementarity problem whose solution provides the closed-loop steady-state periodic oscillation exhibited by the modulated system. The proposed approach can be applied to a wide class of power converters; a DC-DC boost converter with voltage-mode control is considered as an illustrative example.